Integral sliding mode output control of delta operator systems with insensitivity to sampling time jitter

This paper focuses on integral sliding mode output control for linear delta operator systems with insensitivity to sampling time jitter in the case of small sampling times along with unmatched disturbances. A delta-domain integral sliding mode sector can be reached without chattering by employing a novel reaching law to avoid the inherent numerical ill-condition resulting from using the traditional shift-domain model at high sampling rates. Parameter sensitivity function of the transfer function with respect to sampling time jitter is also defined to mitigate the effect of sampling time jitter which may cause significant degradation of the overall system performance. By combining the novel bounded real lemma for delta operator using integral sliding mode adaptive control approach, a method of designing output feedback controller with insensitive to sample time jitter based on linear matrix inequality (LMI) is proposed, where the corresponding reaching law proposed is able to reduce the chattering. Finally, a numerical example is presented to show the effectiveness of the proposed method.